Lecture Eleven The Overall Cost of Capital

1
Lecture ElevenThe Overall Cost of Capital

• Cost of Capital Components
• Debt
• Preferred
• Common Equity
• WACC
• MCC
• IOS

2
Cost of Capital

• 1. For capital budgeting purposes - opportunity
  cost, hurdle rate, cut off rate
• 2. For measure of effective or desirable capital
  structure. ie. Relative merit of varying degrees
  of leverage (D/TA) or (D/E)
• 3. For growth of the economy. If estimate of
  overall cost of capital is higher than the
  actual, investment (I), will be less that is
  economically justified and the economy will slow
  down
• Estimation of the cost of capital for the firm
  is very important but quite difficult to do. So
  we may settle for a range or a worry zone
  concept.

3
Theoretical Definition of the Cost of Capital

• I. Gordons
• The cost of capital for a given firm is a
  discount rate with the property that an
  investment with a rate of profit above (below)
  this rate will raise (lower) the value of the
  firm.
• II. Johnsons
• Financial manager may measure his firms cost of
  capital and his policies may affect the cost of
  capital. But the ultimate determination of the
  cost of capital rest in the market place and is
  established by investors who manage this
  portfolio to achieve what each views as his
  optimal balance between ask and return.
• III. Van Hornes
• In general, the over all cost of capital is the
  discount rate that equates the present value of
  the funds received by the firm, net of
  underwriting and other costs, with the present
  value of expected outflows.

4
The outflows may be

• 1. Interest payments (adjusted for taxes)
• 2. Repayments of principal
• 3. Dividends
• 4. Stock purchases by the firm from its
  shareholders
• In mathematical notation, this definition is
• Where
• Io Net amount of funds received by the firm at
  time zero (known)
• Ct Outflow in period t (known)
• K The discount factor cost of capital
  (unknown, i.e. what you solve for).

5
What types of long-term capital do firms use?

• Long-term debt
• Preferred stock
• Common equity
• Retained earnings
• New common stock

6
Cost of Capital Equations Summary

• Kd cost of new debt --- investment banker
  quote use bond valuation mode solving for Kd
• Kd(1 - T) after tax cost of debt
• Kp cost of preferred stock
• KaWeighted Average Cost of Capital (WACC)
• Kd(1-T)(Wd)Kp(Wp)Ks(Ws) or Ke(We)

7
Should we focus on before-tax or after-tax
capital costs?
Stockholders focus on A-T CFs. Thus, focus on A-T
capital costs, i.e., use A-T costs in WACC.
Only kd needs adjustment.
8
Should we focus on historical (embedded) costs or
new (marginal) costs?
The cost of capital is used primarily to make
decisions which involve raising new capital. So,
focus on todays marginal costs (for WACC).
9
A 15-year, 12 semiannual bond sells for
1,153.72. Whats kd?
0
1
2
30
i ?
...
60
60 1,000
60
-1,153.72
30 -1153.72 60 1000 5.0
x 2 kd 10
INPUTS
PMT
OUTPUT
10
Component Cost of Debt

• Interest is tax deductible, so
• kd AT kd BT(1 - T)
• 10(1 - 0.40) 6.
• Use nominal rate.
• Flotation costs small.
• Ignore.

11
Whats the cost of preferred stock? PP
113.10 10Q Par 100 F 2.
Use this formula
12
Picture of Preferred
ì
0
1
2
kps ?
...
2.50
2.50
-111.1
2.50
13
Note

• Flotation costs for preferred are significant, so
  are reflected. Use net price.
• Preferred dividends are not deductible, so no tax
  adjustment. Just kps.
• Nominal kps is used.

14
Is preferred stock more or less risky to
investors than debt?

• More risky company not required to pay preferred
  dividend.
• However, firms try to pay preferred dividend.
  Otherwise, (1) cannot pay common dividend, (2)
  difficult to raise additional funds, (3)
  preferred stockholders may gain control of firm.

15
Why is yield on preferred lower than kd?

• Corporations own most preferred stock, because
  70 of preferred dividend are nontaxable to
  corporations.
• Therefore, preferred often has a lower B-T yield
  than the B-T yield on debt.
• The A-T yield to an investor, and the A-T cost to
  the issuer, are higher on preferred than on debt.
  Consistent with higher risk of preferred.

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Example
kps 8.84 kd 10 T 40
kps, AT kps - kps (1 - 0.7)(T)
8.84 - 8.84(0.3)(0.4) 7.78
kd, AT 10 - 10(0.4) 6.00
A-T Risk Premium on Preferred 1.78
17
Why is there a cost for retained earnings?

• Earnings can be reinvested or paid out as
  dividends.
• Investors could buy other securities, earn a
  return.
• Thus, there is an opportunity cost if earnings
  are retained.

18

• Opportunity cost The return stockholders could
  earn on alternative investments of equal risk.
• They could buy similar stocks and earn ks, or
  company could repurchase its own stock and earn
  ks. So, ks is the cost of retained earnings.

19
Three ways to determine cost of retained
earnings, ks
1. CAPM ks kRF (kM - kRF)b. 2. DCF ks
D1/P0 g. 3. Own-Bond-Yield-Plus-Risk
Premium ks kd RP.
20
What is the Capital Asset Pricing Model (CAPM)
slides 9-16 to 9-26
sp ()
Company Specific Risk
35
Stand-Alone Risk, sp
20 0
Market Risk
10 20 30 40 2,000
Stocks in Portfolio
21

• As more stocks are added, each new stock has a
  smaller risk-reducing impact.
• sp falls very slowly after about 40 stocks are
  included. The lower limit for sp is about 20
  sM .

22
Stand-alone Market Firm-specific

risk risk risk
Market risk is that part of a securitys
stand-alone risk that cannot be eliminated by
diversification. Firm-specific risk is that part
of a securitys stand-alone risk which can be
eliminated by proper diversification.
23

• By forming portfolios, we can eliminate about
  half the riskiness of individual stocks (35 vs.
  20).

24
If you chose to hold a one-stock portfolio and
thus are exposed to more risk than diversified
investors, would you be compensated for all the
risk you bear?
25

• NO!
• Stand-alone risk as measured by a stocks s or CV
  is not important to a well-diversified investor.
• Rational, risk averse investors are concerned
  with sp , which is based on market risk.

26

• There can only be one price, hence market return,
  for a given security. Therefore, no compensation
  can be earned for the additional risk of a
  one-stock portfolio.

27

• Beta measures a stocks market risk. It shows a
  stocks volatility relative to the market.
• Beta shows how risky a stock is if the stock is
  held in a well-diversified portfolio.

28
Use the SML to calculate therequired returns.
SML ki kRF (kM - kRF)bi .

• Assume kRF 8.
• Note that kM kM is 15. (Equil.)
• RPM kM - kRF 15 - 8 7.

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Expected vs. Required Returns

k
k
HT 17.4 17.0 Undervalued k gt k Market
15.0 15.0 Fairly valued USR 13.8 12.8
Undervalued k gt k T-bills 8.0 8.0 Fairly
valued Coll. 1.7 2.0 Overvalued k lt k



30
SML ki 8 (15 - 8) bi .
ki ()
SML
.
HT
.
.
kM 15 kRF 8
USR
.
T-bills
.
Coll.
Risk, bi
-1 0 1 2
31
Whats the cost of retained earnings based on the
CAPM?kRF 7, MRP 6, b 1.2.
ks kRF (kM - kRF )b.
7.0 (6.0)1.2 14.2.
32
Whats the DCF cost of retained earnings, ks?
Given D0 4.19P0 50 g 5.
33
Suppose the company has been earning 15 on
equity (ROE 15) and retaining 35 (dividend
payout 65), and this situation is expected to
continue.Whats the expected future g?
34
Retention growth rateg b(ROE) 0.35(15)
5.25.Here b Fraction retained.Close to g
5 given earlier. Think of bank account paying
10 with b 0, b 1.0, and b 0.5. Whats g?
35
Could DCF methodology be applied if g is not
constant?

• YES, nonconstant g stocks are expected to have
  constant g at some point, generally in 5 to 10
  years.
• But calculations get complicated.

36
Find ks using the own-bond-yield-plus-risk-premium
method. (kd 10, RP 4.)
ks kd RP 10.0 4.0 14.0

• This RP CAPM RP.
• Produces ballpark estimate of ks. Useful check.

37
Whats a reasonable final estimate of ks?
38
How do we find the cost of new common stock, ke?
Use DCF formula, but adjust P0 for flotation
cost. End up with ke gt ks.
39
New common, F 15
40
Flotation adjustment ke - ks 15.4 - 13.8
1.6.
Add the 1.6 flotation adjustment to average ks
14 to find average ke
ke ks Floatation adjustment
14 1.6 15.6.
41
Why is ke gt ks?
1. Investors expect to earn ks. 2. Company gets
money as retained earnings earns ks
everythings O.K. 3. But investors put up money
to buy new stock F pulled out so net money
must earn gt ks to provide ks on money investors
put up.
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Example
1. ks D1/P0 g 10 F 20. 2. Investors
put up 100, expect EPS DPS 0.1(100)
10. 3. But company nets only 80. 4. If earn ks
10 on 80, EPS DPS 0.10(80) 8. Too
low. Price falls. 5. Need to earn ke 10 /0.8
12.5. 6. Then EPS 0.125(80)
10. Conclusion ke 12.5 gt ks 10.0.
43
Whats WACC using only retained earnings for
equity component of WACC1?
WACC1 wdkd(1 - T) wpskps wceks
0.3(10)(0.6) 0.1(9) 0.6(14) 1.8 0.9
8.4 11.1. Cost per 1 until retained
earnings used up.
44
WACC with New CS
F 15
WACC2 wdkd(1 - T) wpskps wceke
0.3(10)(0.6) 0.1(9) 0.6(15.6) 1.8
0.9 9.4 12.1.
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Summary to this Point
WACC rises because equity cost is rising.
46
MCC Schedule Definition

• MCC shows cost of each dollar raised.
• Each dollar consists of 0.30 of debt, 0.10 of
  Preferred and 0.60 of equity (retained earnings
  or new sommon stock).
• First dollars cost WACC1 11.1, then WACC2
  12.1.

47
How large will capital budget be before must
issue new CS?
Capital Budget Capital Raised
Debt 0.3 Capital Raised Preferred
0.1 Capital Raised Equity 0.6
Capital Raised 1.0 Total Capital
Equity RE 0.6 Capital Raised, so
Capital Raised RE/0.6.
48
Find Retained Earnings Break Point
Dollars of RE Fraction of equity
BPRE
300,000 0.60
500,000.
500,000 total can be financed with retained
earnings, debt, and preferred.
49
WACC ()
WACC1 11.1
15
WACC212.1
10
500 2,000
Dollars of New Capital (in thousands)
50
Investment Opportunities(Capital Budgeting
Projects)
Which to accept?
51

A 17
B 15
MCC
12.1
C 11.5
11.1
IOS
Optimal Capital Budget
500
1,200
2,000
52

• Projects A and B would be accepted (IRR exceeds
  the MCC).
• Project C would be rejected (IRR is less than the
  MCC).
• Capital Budget 1.2 million.

53
Would the MCC remain constant beyond 2 million?

• No. WACC would eventually rise above 12.1.
• Costs of debt, preferred stock would rise.
• Large increases in capital budget may also
  increase the perceived risk of the firm,
  increasing WACC.